Field of the Invention
Embodiments described herein relate to 3-Dimensional (3-D) printing, and more particularly, to a method and apparatus for preserving structural integrity of 3-D models when printing at varying scales.
Description of the Related Art
3-D printing is an “additive” manufacturing process, where a 3-D printer operates like a layering machine. Each layer can be considered a 2-Dimensional (2D) (x-y) area quantized into discrete points of data laid down by a “print head” of the 3-D printer. The print head can emit light or material in a raster or grid format (i.e., x-y). Each point, and therefore each 2D layer, typically also has a uniform height z. For printing a 3-D model in an x-y-z voxel grid, multiple 2D layers of quantized data of height z are additively combined one above the other (or below the other, depending on the specific type of 3-D printing process used), thereby manufacturing the 3-D model in a layer by layer process. Although an original mesh format of the 3-D model contains infinite data, upon conversion of the 3-D surface data into layers for 3-D printing, as described below, there is a necessary loss of data integrity due to quantization errors and alignment effects during the digital conversion and the layered printing process. Accordingly, fine details in the 3-D model may not be faithfully reproduced upon printing.
More specifically, if the layer thickness capability of the 3-D printer is 250 μm, and a detail of the 3-D model has a height in the z-axis direction of the voxel grid of 1000 μm, only four (that is, 1000/250) layers of voxel grid data would be available to reproduce that 1000 μm detail. Limitation to only four layers will obviously lead to a jagged and unfaithful reproduction of any portion of the 1000 μm detail that is not aligned with the z axis of the voxel grid. However, if the 3-D printing process included voxel layers of 15 μm each in the z-axis direction of the voxel grid, 66 layers (1000/15) of voxel grid data would be available to incrementally reproduce any portion of the 1000 μm detail that is not aligned with the z axis of the voxel grid. Thus, providing 66 layers to follow the details of the 3-D model in the z-axis direction instead of only 4 layers results in a more faithful reproduction of details of the 3-D model. Similarly, quantization and alignment errors in the x-axis and y-axis directions between the voxelized 3-D model and the voxel grid upon printing will also lead to unfaithful reproduction. As well known by those of ordinary skill in the art, quantization errors are “rounding off” errors that result when quantizing (converting) a value in a digital domain. Alignment errors in this context are position effects that result when attempting to align two different coordinate axis, such as the x, y, z axis of a volume representation of a 3-D model, with the x, y, z voxel grid that the head of a 3-D printer is constrained to follow when printing due to its physical design. Both of the quantization errors and the alignment errors can become exacerbated in dependence on differences of scale between the volume representation of the 3-D model and the voxel grid of the 3-D printer.
The possibility for unfaithful reproduction is even further complicated by the fact that 3-D printer software typically allows a user to select a desired scale upon printing, so as to adjust the size of the printed 3-D model. Changing the size of the 3-D model to be printed necessarily affects the size of the details to be reproduced, but does not change the amount of layers that the printer has in order to reproduce those details. As noted by the example above, a model with fewer layers leads to the possibility of increased quantization errors and alignment errors.
Therefore, there is a need for a method and apparatus for preserving structural integrity of 3-D models when printing at varying scales.